On the structure of covariant phase observables

Abstract

We study the mathematical structure of covariant phase observables. Such an observable can alternatively be expressed as a phase matrix, as a sequence of unit vectors, as a sequence of phase states, or as an equivalent class of covariant trace-preserving operations. Covariant generalized operator measures are defined by structure matrices which form a W*-algebra with phase matrices as its subset. The properties of the Radon-Nikodym derivatives of phase probability measures are studied.

11 pages

References in corpus (2)

• Covariant localizations in the torus and the phase observables
• The Pegg-Barnett Formalism and Covariant Phase Observables

Cited by in corpus (6)

• The canonical phase measurement is pure
• Regular phase operator and SU(1,1) coherent states of the harmonic oscillator
• Covariant phase difference observables
• Optimal covariant measurements: the case of a compact symmetry group and phase observables
• On infinite matrices, Schur products, and operator measures
• The phase representation of covariant phase observables